{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IA6JTRE3JATI3OVIUMAWGENO4X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4e6ee3fc5e11ce69472ad837aef88eddd5a13f43006f0507b5dea04a8e8f5539","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-26T13:19:04Z","title_canon_sha256":"6f238b69f85588a3c5afa8f27b4507db32618dbcecb6dc6bbc0cc98af3a5219f"},"schema_version":"1.0","source":{"id":"1104.4914","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4914","created_at":"2026-05-18T04:20:24Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4914v1","created_at":"2026-05-18T04:20:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4914","created_at":"2026-05-18T04:20:24Z"},{"alias_kind":"pith_short_12","alias_value":"IA6JTRE3JATI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IA6JTRE3JATI3OVI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IA6JTRE3","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:f1a6485d8095605d43cbbffec8c7ab9eaab5790c745c09c61b46ba88f36ae2a4","target":"graph","created_at":"2026-05-18T04:20:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a \"measure\" problem that results from improper weighting of phase space. This issue is addressed considering a generic collision process whereby a large number of particles/agents randomly and repeatedly interact in pairs, with prescribed conservation law(s). We find a sufficient condition under which the stationary single particle distribution function maximizes an entropy-like functional, that is free of the measure problem. This condition amounts to a factoriz","authors_text":"E. Trizac, P. Maynar","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-26T13:19:04Z","title":"Entropy of continuous mixtures and the measure problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4914","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:902248d079ab4430ecf58360e41792d3d546e147fb47a4b9658ffdc201c4ac58","target":"record","created_at":"2026-05-18T04:20:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4e6ee3fc5e11ce69472ad837aef88eddd5a13f43006f0507b5dea04a8e8f5539","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-26T13:19:04Z","title_canon_sha256":"6f238b69f85588a3c5afa8f27b4507db32618dbcecb6dc6bbc0cc98af3a5219f"},"schema_version":"1.0","source":{"id":"1104.4914","kind":"arxiv","version":1}},"canonical_sha256":"403c99c49b48268dbaa8a3016311aee5c068bdbf00568c2dd95e98952cb6ffb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"403c99c49b48268dbaa8a3016311aee5c068bdbf00568c2dd95e98952cb6ffb2","first_computed_at":"2026-05-18T04:20:24.511912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:24.511912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nNs2rko2GkToebGJlFFsNGJNbbQG7kUS5NPseO1Bg0XbAZBaHTj4nvAIMqeNxoaeT8A27Uet3otrdMq+NIzIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:24.512463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4914","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:902248d079ab4430ecf58360e41792d3d546e147fb47a4b9658ffdc201c4ac58","sha256:f1a6485d8095605d43cbbffec8c7ab9eaab5790c745c09c61b46ba88f36ae2a4"],"state_sha256":"842d9aac0973e0669564061a21876823999184869d63b5a6ad2d39af9eb194d3"}